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| ``Wieferich prime''
by bert on 2005-12-17 08:21:48 |
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| This entry is out-of-date. Also it has a misprint, defining it as a prime whose square does not divide 2^p - 1.
The only Wieferich primes known are 1093 and 3511. It is currently unknown whether or not there are infinitely many of them, but there are no others less than 1.25 x 10^15 (McIntosh 2004; see http://www.loria.fr/~zimmerma/records/Wieferich.status). It has been proved that the ABC conjecture implies that there are infinitely many primes that are not Wieferich (J. Silverman, "Wieferich's Criterion and the abc Conjecture", J. Number Th. 30 (1988) 226-237). |
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